2/7 | 2/8 | 2/9 | 2/10 | 3/6 | 3/7 | 3/8 | 3/9 | 4/3 | 4/3 | 4/4 | 4/5 | 5/1 | 5/2 | 5/3 | 5/4 | ||||||||
1/19 | 1/20 | 2/14 | 2/15 | 2/16 | 2/17 | 3/13 | 3/14 | 3/15 | 3/16 | 4/10 | 4/11 | 4/12 | 4/13 | ||||||||||
1/24 | 1/25 | 1/26 | 1/27 | 2/21 | 2/22 | 2/23 | 2/24 | 3/20 | 3/21 | 3/22 | 3/23 | 4/17 | 4/18 | 4/19 | 4/20 | ||||||||
1/31 | 2/1 | 2/2 | 2/3 | 2/28 | 2/29 | 3/1 | 3/2 | 3/27 | 3/28 | 3/29 | 3/30 | 4/24 | 4/25 | 4/26 | 4/27 |
5. Boyle's law states that , for a certain gas P*V = 320, where P is
pressure and V is volume.
A. Draw a complete graph representing this situation.
Label your axes and write an equation for each asymptote.
Make a table of values for P and V using P=320/V and P>0, V>0.
V | P |
80 | 4 |
160 | 2 |
320 | 1 |
640 | .5 |
Now use these data points to sketch the graph.
B. If 8 < V < 40, what are the corresponding values of
P?
Notice that when V=8, P = 40 and when V=40, P= 8. So as V varies from
8 to 40, P varies from 40 to 8.
With this definition we have
g(0)=5, g(1)=6, g(-1)=6,g(2)=9, g(1/2)=21/4, g(t)=t^{2}+5,
g(1+t)=(1+t)^{2}+5, etc.
x | f(x) |
2 | 5 |
1 | 3 |
0 | -2 |
-1 | 4 |
-2 | 0 |
x | L | A |
10 | 120 | 1200 |
20 | 100 | 2000 |
70 | 0 | 0 |
60 | 20 | 1200 |
50 | 40 | 2000 |
In fact, A = -2x^{2}+140x but A also can be expressed
by A= -2(x-35)^{2} +2450. It should be clear from thinking about
this expression for A that A is at most 2450, since for any x other than
35, A will be the result of subtracting a positive number from 2450.
Example: Average cost= C(x)/x
Average Velocity Example: Suppose
position of an anvil falling from a 100 foot cliff is a function of time,
S = -16t^{2} +100 feet
at time t seconds.
The position at times t=1 and t=2.
Find the average velocity during
the time interval [1,2].
Solution: S(1) = -16+100 = 84;
S(2) = -16*4 + 100 = 36.
Average velocity = change in position/
change in time = [S(2)-S(1)]/[2-1] = (36-84)/(2-1) = -48 ft/sec.
Note: The negative velocity indicates
the anvil is falling down. The average speed of the anvil is 48 ft/sec.
The slope of the secant line is [f(a+h)-f(a)]/h.
This is also the average velocity of an object moving on a straight line with its position S = f(t) at time t for the time interval between time time t= a and time t=a+h.
Now: THINK! When h ->0, this slope = -64-16h -> -64. Thus the slope is -64.